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Compare each row values in second table in SQL Server?

I have a scenario where I have to search value of column 1 in first table to see whether it matches some value in another table.

This should continue in a loop until the last row on first table has been compared.

No loops needed. You can do this easily as a set based operation using exists()

select * 
  from FirstTable
  where exists (
  select 1 
    from SecondTable 
    where FirstTable.Column1 = SecondTable.Column1
    );

To find the opposite, where the row in the first table does not have a match based on Column1, you can use not exists()

select * 
  from FirstTable
  where not exists (
  select 1 
    from SecondTable 
    where FirstTable.Column1 = SecondTable.Column1
    );

If you want to identify which rows have a match and don't you can use:

select FirstTable.*
    , MatchFound = case when x.Column1 is null then 'No' else 'Yes' end
    , x.Column1
  from FirstTable 
  outer apply (
    select top 1 
        *
    from SecondTable 
    where FirstTable.Column1 = SecondTable.Column1
      ) as x

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